'Total return is the amount of value an investor earns from a security over a specific period, typically one year, when all distributions are reinvested. Total return is expressed as a percentage of the amount invested. For example, a total return of 20% means the security increased by 20% of its original value due to a price increase, distribution of dividends (if a stock), coupons (if a bond) or capital gains (if a fund). Total return is a strong measure of an investment’s overall performance.'

Which means for our asset as example:- The total return, or increase in value over 5 years of ProShares UltraPro QQQ is 1385.6%, which is higher, thus better compared to the benchmark SPY (128%) in the same period.
- Looking at total return, or performance in of 262.2% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (44.9%).

'The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (17.9%) in the period of the last 5 years, the annual performance (CAGR) of 71.5% of ProShares UltraPro QQQ is higher, thus better.
- Compared with SPY (13.2%) in the period of the last 3 years, the annual return (CAGR) of 53.6% is larger, thus better.

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (18.7%) in the period of the last 5 years, the historical 30 days volatility of 64.5% of ProShares UltraPro QQQ is higher, thus worse.
- During the last 3 years, the 30 days standard deviation is 77.3%, which is greater, thus worse than the value of 22.9% from the benchmark.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Using this definition on our asset we see for example:- The downside deviation over 5 years of ProShares UltraPro QQQ is 46.1%, which is larger, thus worse compared to the benchmark SPY (13.6%) in the same period.
- Compared with SPY (16.7%) in the period of the last 3 years, the downside risk of 55.7% is higher, thus worse.

'The Sharpe ratio is the measure of risk-adjusted return of a financial portfolio. Sharpe ratio is a measure of excess portfolio return over the risk-free rate relative to its standard deviation. Normally, the 90-day Treasury bill rate is taken as the proxy for risk-free rate. A portfolio with a higher Sharpe ratio is considered superior relative to its peers. The measure was named after William F Sharpe, a Nobel laureate and professor of finance, emeritus at Stanford University.'

Which means for our asset as example:- The ratio of return and volatility (Sharpe) over 5 years of ProShares UltraPro QQQ is 1.07, which is higher, thus better compared to the benchmark SPY (0.82) in the same period.
- Looking at ratio of return and volatility (Sharpe) in of 0.66 in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (0.47).

'The Sortino ratio, a variation of the Sharpe ratio only factors in the downside, or negative volatility, rather than the total volatility used in calculating the Sharpe ratio. The theory behind the Sortino variation is that upside volatility is a plus for the investment, and it, therefore, should not be included in the risk calculation. Therefore, the Sortino ratio takes upside volatility out of the equation and uses only the downside standard deviation in its calculation instead of the total standard deviation that is used in calculating the Sharpe ratio.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (1.14) in the period of the last 5 years, the ratio of annual return and downside deviation of 1.5 of ProShares UltraPro QQQ is greater, thus better.
- During the last 3 years, the downside risk / excess return profile is 0.92, which is higher, thus better than the value of 0.64 from the benchmark.

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Applying this definition to our asset in some examples:- The Ulcer Index over 5 years of ProShares UltraPro QQQ is 18 , which is higher, thus worse compared to the benchmark SPY (5.59 ) in the same period.
- Compared with SPY (7.15 ) in the period of the last 3 years, the Downside risk index of 23 is higher, thus worse.

'Maximum drawdown is defined as the peak-to-trough decline of an investment during a specific period. It is usually quoted as a percentage of the peak value. The maximum drawdown can be calculated based on absolute returns, in order to identify strategies that suffer less during market downturns, such as low-volatility strategies. However, the maximum drawdown can also be calculated based on returns relative to a benchmark index, for identifying strategies that show steady outperformance over time.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum drop from peak to valley of -69.9 days of ProShares UltraPro QQQ is lower, thus worse.
- During the last 3 years, the maximum DrawDown is -69.9 days, which is smaller, thus worse than the value of -33.7 days from the benchmark.

'The Maximum Drawdown Duration is an extension of the Maximum Drawdown. However, this metric does not explain the drawdown in dollars or percentages, rather in days, weeks, or months. It is the length of time the account was in the Max Drawdown. A Max Drawdown measures a retrenchment from when an equity curve reaches a new high. It’s the maximum an account lost during that retrenchment. This method is applied because a valley can’t be measured until a new high occurs. Once the new high is reached, the percentage change from the old high to the bottom of the largest trough is recorded.'

Applying this definition to our asset in some examples:- Looking at the maximum time in days below previous high water mark of 296 days in the last 5 years of ProShares UltraPro QQQ, we see it is relatively higher, thus worse in comparison to the benchmark SPY (139 days)
- During the last 3 years, the maximum time in days below previous high water mark is 296 days, which is larger, thus worse than the value of 139 days from the benchmark.

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Avg Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum duration it does not measure only one drawdown event but calculates the average of all.'

Which means for our asset as example:- Compared with the benchmark SPY (33 days) in the period of the last 5 years, the average days below previous high of 56 days of ProShares UltraPro QQQ is greater, thus worse.
- Compared with SPY (45 days) in the period of the last 3 years, the average time in days below previous high water mark of 80 days is larger, thus worse.

Historical returns have been extended using synthetic data.
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- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of ProShares UltraPro QQQ are hypothetical, do not account for slippage, fees or taxes, and are based on backtesting, which has many inherent limitations, some of which are described in our Terms of Use.